Engineering Mechanics

(^644) „„„„„ A Textbook of Engineering Mechanics
EXERCISE 31.2

1. A body of mass 20 kg is suspended by a light string wound round a pulley of mass 50 kg.
   Find acceleration of the body and pull in the string. [Ans. 4.36 m/s^2 ; 108.9 N]


2. A body of mass 22.5 kg is hanging by a light cord from a frictionless wheel and axle of
   mass 45 kg as shown in Fig. 31.17. After 16 seconds of the release of the hanging mass
   from rest, the wheel was found to be revolving with an angular velocity of 144 r.p.m.

Fig. 31.14.

From first principles, find the moment of inertia of the wheel and axle.

[Ans. 11.64 kg-m^2 ]

3. A light rope passing round a pulley of mass 60 kg, radius 300 mm and radius of gyration
   200 mm, has two masses 8 kg and 6 kg attached to its ends. If the rope does not slip as the
   pulley rotates, determine the acceleration of the two masses and the pulls in the two
   ropes. [Ans. 0.48 m/s^2 ; 74.6 N; 61.7 N]


4. Two masses of 100 kg and 40 kg are supported by a rope of negligible mass passing over
   a solid disc pulley. If the mass of the pulley is 50 kg, find the acceleration of the 100 kg
   mass and the pulls in the two strings. [Ans. 3.56 m/s^2 ; 624 N; 534.4 N]
   Hint. For a solid disc pulley of radius r,
   k^2 = 0.5 r^2
   ∴ Mass moment of inertia,
   I=Mk^2 = 50 × 0.5 r^2 = 25 r^2

31.20.MOTION OF A BODY ROLLING ON A ROUGH HORIZONTAL PLANE

WITHOUT SLIPPING

Fig. 31.15. Body rolling on a rough horizontal plane without slipping.

Consider a body A tied to a string passing over a smooth pulley and pulling another circular

body B, which rolls on a rough horizontal plane without slipping as shown in Fig. 31.14 (a).